The use of the conservation of living force before Helmholtz

Abstract

In his recent authoritative Helmholtz and the Conservation of Energy, Kenneth Caneva has claimed that earlier authors had invoked the principle of conservation of living force only in cases of a system returning to an earlier state, or of one without Newtonian forces. Relaying on texts in the tradition of the French Analytical Mechanics form Lagrange to Coriolis, I argue that this was not the case, and that the principle had been formulated and used for cases where living force proper (mv²) was not conserved but its sum with an integral function (refers today as potential) was constant. In addition. I show that contrary to Caneva's claim, the principle had been connected to the impossibility of creating power out of nothing. The two points indicate a stronger link between the analytical tradition and Helmholtz and his readers than usually portrayed, and the significant contribution of mechanics to the emergence of energy conservation. On a methodological level the use of living force shows that a common term and even a concept, like energy, is not always needed for its successful employment.

Keywords: Claude Louis Navier; Energy conservation; Joseph Louis Lagrange; analytical mechanics; conservation of vis viva.